It’s really simple: you send a query letter. Companies DO NOT want to see your screenplay; that is the “unsolicited material” they don’t accept. They’ll accept query letters all day long. Do your due diligence: find out who you contact, and send your query letter specifically to that person (or department). That’s the professional way …
Writers don’t need publishing companies. They haven’t needed publishing companies for more than a decade. Writers also shouldn’t self-publish. With the maturation of the indie publishing community, there are professionals (the exact same professionals who work for publishing companies) who can help any anyone with a manuscript go from writer to author.